Multiple wordpress site installation

Data size doesn’t have to slow the site. It becomes a matter of how fast can you get the data from the DB. A few things to consider:

1. Place the Database on a dedicated host. If locally hosted dedicate a crossover cable from the web tier to the DB tier, with a second IP for admin on the database host. You might consider a managed instance of your database with a cloud provider.
2. Indexes are your friend. Larger datasets result in longer indexes, but you can make deliberately shortened indexes. Choose a database that supports partitioned indexes. Combine these partitioned indexes along with higher I/O operations per second of SSDs for your index partitions and ensuring that all lookup access via index will result in your performance for large data sets doesn’t suffer. How does a partitioned index increase access speed? Instead of having to traverse an index from A to S for an index supported query with an S based where clause, in a partioned index you might have 26 indexes, one for A, then B, then C, then … You jump straight to the S partition for the lookup.
3. Shape your pool size on the PHP/Web tier. You have already increased the pool size by pulling the database onto its own host. The next thing to do is to effectively manage your cache of fixed assets, the items that do not change across user sessions. Commonly these items are style sheets, images, fonts, javascript files, … Minimally look at a cache node in front of your wordpress site. Take a look at Varnish or Nginx for this. I am partial to Varnish, but either should do the trick. If you pair this with a CDN for a multigenerational cache then all the better. If you are in the cloud then you have built in CDN options with each cloud provider. You can also widen your bandwidth by placing these fixed assets ona dedicated host and then caching that one host, but this would require a lot of base modification of your wordpress image.
4. There is no reason why you cannot have multiple web fronts with a common database back end. You would need a load balancer to distribute the load and your first generation cache would sit in front of the load balancer. Realistically, if all of your queries are index supported and your cache is effectively managed, then you can easily scale to hundreds of concurrent users on moderate hardware. Your most taxing item is going to be your PHP execution to pull dynamic data for user sessions. Make the queries respond as fast as possible then you have a small lock window on PHP for each session.
5. Watch your locks per session! You may be at the mercy of a template and how it is managing your finite resource pool, but in general (a) unless 50%+1 use something, do not allocate it early, (b) be merciless in cutting sessions to release the session based locks on memory, (c) pinch your assets until they bleed – No 45 MB images on the front page when a color optimized 120K compressed image will do the job, (d) Watch the repeat access problem – This applies to subqueries in the database as well as building a web page with hundreds of assets to resolve a page.
6. Have you considered other options, such as Drupal? The setup is a bit more complex, but I can validate running a dozen distinct websites out of a single Drupal instance with no degradation in performance with the above dedicated database and cache nodes with hundreds of concurrent users on fairly moderate hardware (mini-itx atom based PCs)